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Homework Help: Number of modes in incoming light

  1. Jul 23, 2006 #1
    Hello all,

    if I have incoming radiation from a blackbody source filtered to a bandwidth of 0.1 nm and centered at a wavelength of 500 nm, why is the number of modes in this light not equal to the density of photon states times the bandwidth?

    I.e why isn't it
    [tex]\text{number of modes} = g(\omega) * \delta \omega = \frac{\omega^2}{\pi^2 c^3} \delta \omega[/tex]
    [tex]\omega = \frac{2 \pi c}{500 nm}[/tex]
    [tex]\delta \omega = \frac{2 \pi c}{0.1 nm}[/tex] ?

    If anyone knows why I'd be very thankful for an explanation.

    Best regards,
  2. jcsd
  3. Jul 23, 2006 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    You're omitting the [itex]exp(\hbar \omega/kT ) - 1 [/itex] factor in the denominator, which comes from the occupation fraction of a Bose gas, if you are interested in the number of occupied states and not just the number of available states.
  4. Jul 26, 2006 #3
    Yes but I thought that adding that factor would give me the number of photons? And that the there are more than one photon for every mode (frequency). Or have I missunderstood the question? I thought that "mode" refers to the number of available frequency states?

    I can't say I've fully grasped the difference between "state", "mode" etc yet
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